If memory serves, there was a Manhasset Hotel on Shelter Island (on the north shore of Shelter Island, near the modern day Gardiner Way) that burned down in the early 1900s --named for the Manahasit Native American tribe local to the area; the town of Manhasset that is quite a bit west of Shelter Island on the north shore of Long Island was also named after them.

I believe there were even some old photos of the hotel posted here a while back.

Yup; Long Island I'm good at; spelling, not so much. Lots of locales on Long Island named with variations of the local Native American tribes of the area.

The house pictured can also be found at this address: 8 Gardiner Way, Dering Harbor, New York.

[Further research reveals that the village at the time was called Manhanset Manor (location of the Manhanset House and Cottages resort); in 1915 the name was changed to Dering Harbor. The Library of Congress errs in correcting the place name "Manhanset" to "Manhasset" in these Shelter Island captions; Manhasset is much farther west on Long Island, in Nassau County. The item below is from the Oct. 30, 1915, issue of Brooklyn Life. - Dave]

I'm having some trouble making sense of the address given in the description here. In the present day, at least, Manhasset and Patchogue Avenue are in two very different parts of Long Island. And Shelter Island sits even farther away, out between the forks at the far eastern end of Long Island.